When Don Albers talks, you had better listen: what he says just might improve the book you were going to write. In 2002, he asked the following question of author Jeff Suzuki: “What would Newton see, if he looked out his window?” Suzuki thought about that discussion a great deal and what emerged was Mathematics in Historical Context. This is a different look at the history of our subject. For the author understands that history is more than facts, historical facts and chronologies — names, dates and places. It is also causes, explanations and interpretations — motivations, reasons and outcomes.

Suzuki takes us on a roughly chronological tour of mathematical achievements from prehistory to the end of World War II. What we read is alternately exhilarating and depressing. On the one hand we see mathematicians producing superior results under grim working conditions, such as Poncelet developing projective geometry while a prisoner of war in Russia. We meet enlightened rulers who understand the wisdom of making their lands a hospitable place in which scholars can work — al Mamun’s establishment of the House of Wisdom in Baghdad, Ptolemy Soter’s founding the Library and the Museum in Alexandria. On the other hand, the necessary historical context is one of politics, so we witness the clash of nation states, the rise and fall of empires, and wars — so many wars.

One example of the author’s point of view is the story of Archimedes. In most histories, we read about his towering achievements, learn a bit about his life and a bit more about the legends (the bathtub and his defense of Syracuse during a siege). But here, we learn a great deal about the Punic Wars, that series of terrible wars that ended with the destruction of Carthage and established the domination of Rome. This provides the context for us to understand what was behind Archimedes’ achievements during the siege of Syracuse.

Another example comes from the Renaissance. We read about the motivations behind the many conflicts among the Italian city-states during the sixteenth century, conflicts that involved France, Spain, the Holy Roman Empire, the Papacy, Venice, and Milan. In 1512 the French invaded the city of Brescia, and unlike many communities, the Brescians fought back. The French promptly massacred 8000 Brescians, and among the wounded was a young boy who was slashed across the face by a French soldier. That boy was Niccolò Fontana, who recovered but was left with a speech impediment, which explained his nickname: Tartaglia, the Stammerer. Of course, Tartaglia was one of the principal figures in the mathematical drama surrounding the first algebraic solution of the cubic. The background Suzuki provides helps the reader both to understand the times and to better appreciate Tartaglia’s achievements.

Finally, this book is highly readable. The author writes well, and his compelling style is marked by felicitous turns of phrase. For example, concerning the plague and the Great Fire of London in 1666, we read this on p. 226: “The fire burned for three days … only eight people are known to have died, and the fire burned the thatch that housed the rats that had the fleas that carried the plague, helping bring an end to the epidemic.”

In short, I highly recommend this worthy book to mathematicians, historians of mathematics, and students of these subjects.

Ezra Brown (ezbrown@math.vt.edu) is Alumni Distinguished Professor of Mathematics at Virginia Tech, with degrees from Rice and LSU. He is a number theorist by trade, a historian of mathematics by temperament, and a fairly regular contributor to the MAA journals. He sings (everything from blues to opera), plays a tolerable jazz piano, and his wife Jo is teaching him to be a gardener. He occasionally bakes biscuits for his students.